Surfaces scattering potentials

In the case of LiF, the measured surface Debye temperatures are usually in the range between 320 and 370 K [79-81]. With d Bulk = this corresponds to an enhancement of the MSA at the liF(OOl) surface by a factor of 3.9-5.2. For NaCl(OOl) surfaces, the measured value for DSurf 250 30K [27, 80). From this, an enhancement of the surface MSAs by a factor of 1.6 is deduced. It is worth mentioning that although should be a unique property of the substrate material, the measured surface Debye temperatures depend to some extent on the type of the scattered particles and, moreover, on the details of the particle-surface scattering potential [81]. 

The summation of pair-wise potentials is a good approximation for molecular dynamics calculations for simple classical many-body problems [27], It has been widely used to simulate hyperthennal energy (>1 eV) atom-surface scattering ... 

Just as in gas phase kinetics, reactive molecular beam-surface scattering is providing important molecular level insight into reaction dynamics. There is no surface reaction for which such studies have proven more illuminating than the carbon monoxide oxidation reaction. For example Len, Wharton and co-workers (23) found that the product CO exits a 700K Pt surface with speeds characteristic of temperatures near 3000K. This indicates that the CO formed by the reactive encounter of adsorbed species is hurled off the surface along a quite repulsive potential. 

For crystals which have flat faces which extend for a fraction of 1 ym, a new type of phenomenon may be observed. Electrons incident at the edge of the crystal parallel to the surface may be channelled along the surface. The potential field of the crystal extending into the vacuum deflects the electrons so that they tend to enter the surface but they are scattered out of the crystal by the surface atoms or by diffraction from the crystal lattice planes parallel to the surface. If the scattering angle is less than the critical angle for total external reflection, the scattered electrons can not surmount the external potential barrier and are deflected back into the crystal (figure 4 (a)). 

The nautre of the He-surface interaction potential determines the major characteristics of the He beam as surface analytical tool. At larger distances the He atom is weakly attracted due to dispersion forces. At a closer approach, the electronic densities of the He atom and of the surface atoms overlap, giving rise to a steep repulsion. The classical turning point for thermal He is a few angstroms in front of the outermost surface layer. This makes the He atom sensitive exclusively to the outermost layer. The low energy of the He atoms and their inert nature ensures that He scattering is a completely nondestructive surface probe. This is particularly important when delicate phases, like physisorbed layers, are investigated. 

Based on the first-principles study of helium adsorption on metals (Zaremba and Kohn, 1977), Esbjerg and Nprskov (1980) made an important observation. Because the He atom is very tight (with a radius about 1 A), the surface electron density of the sample does not vary much within the volume of the He atom. Therefore, the interaction energy should be determined by the electron density of the sample at the location of the He nucleus. A calculation of the interaction of a He atom with a homogeneous electron distribution results in an explicit relation between the He scattering potential V r) and the local electron density p(r). For He atoms with kinetic energy smaller than 0.1 eV, Esbjerg and Nprskov (1980) obtained... 

Esbjerg, N., and Nprskov, J. K. (1980). Dependence of the He-scattering potential at surfaces on the surface-electron-density profile. Phys. Rev. Lett. 45, 807-810. 

A thermal energy atomic beam (20-200 meV) has a wavelength on the order of inter-atomic distances. The atomic beam diffracts from a contour of the surface potential corresponding to the beam energy. This contour is located 3-4 A above the ion cores in the outermost layer of the surface. Atomic beam diffraction patterns are normally interpreted using model surface scattering calculations, where the scattering is described as a Van der Waals interaction. 

Here P( R ) is the scattering potential for the ensemble of scatters at locations R G is the free-space electron propagator and T0 the f-matrix for multiple scattering of the electron by the surface. 

Electrophoretic light scattering (ELS) is commonly used to measure v. The electrophoretic mobility /r can be calculated from v and the known value of E according to Eq. (I). Theoretical models [ I.7-I0] that describe colloidal electrostatics and hydrodynamics can then be used to relate the measured values of n to particle electrical characteristics including surface charge density and surface electric potential. Because /r depends on the surface electrostatic properties but not particle bulk properties, ELS can characterize surface electrostatic properties exclusively for a wide range of colloidal materials. 

Another important area in which X-ray surface scattering is applied is the underpotential deposition of metals. Underpotential deposition is the phenomenon by which one metal deposits on another at a potential positive of its normal reduction potential. For example, Pb deposits at underpotentials on Ag. This is due to the fact that the Gibbs energy for formation of a Pb-Ag bond is less than that for formation of a Pb-Pb bond. Other metals which undergo underpotential deposition on Ag, Au, and Pt are T1 and Bi. On the basis of the electrochemistry observed in formation of the metal monolayers, there is good reason to expect that they are well ordered. Tl, Pb, and Bi all form an incommensurate monolayers on Au(lll). On Au(lOO), Tl and Bi form an incommensurate monolayer with a c(2 X 2) surface structure [14]. On the other hand, underpotential deposition of Pb on Ag(lll) leads to an incommensurate monolayer [13]. These studies demonstrate clearly that the nature of the monolayer formed depends on both the nature and structure of the substrate metal. 

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